This article provides an overview of recent results on lexicographic, linear, and Bayesian models for paired comparison from a cognitive psychology perspective. Within each class, we distinguish subclasses according to the computational complexity required for parameter setting. We identify the optimal model in each class, where optimality is defined with respect to performance when fitting known data. Although not optimal when fitting data, simple models can be astonishingly accurate when generalizing to new data. A simple heuristic belonging to the class (...) of lexicographic models is Take The Best (Gigerenzer & Goldstein (1996) Psychol. Rev. 102: 684). It is more robust than other lexicographic strategies which use complex procedures to establish a cue hierarchy. In fact, it is robust due to its simplicity, not despite it. Similarly, Take The Best looks up only a fraction of the information that linear and Bayesian models require; yet it achieves performance comparable to that of models which integrate information. Due to its simplicity, frugality, and accuracy, Take The Best is a plausible candidate for a psychological model in the tradition of bounded rationality. We review empirical evidence showing the descriptive validity of fast and frugal heuristics. (shrink)

Humans and animals make inferences about the world under limited time and knowledge. In contrast, many models of rational inference treat the mind as a Laplacean Demon, equipped with unlimited time, knowledge, and computational might. Following H. Simon's notion of satisficing, the authors have proposed a family of algorithms based on a simple psychological mechanism: one-reason decision making. These fast and frugal algorithms violate fundamental tenets of classical rationality: They neither look up nor integrate all information. By computer simulation, the (...) authors held a competition between the satisficing "Take The Best" algorithm and various "rational" inference procedures. The Take The Best algorithm matched or outperformed all competitors in inferential speed and accuracy. This result is an existence proof that cognitive mechanisms capable of successful performance in the real world do not need to satisfy the classical norms of rational inference. (shrink)

The general problem of forming composite variables from components is prevalent in many types of research. A major aspect of this problem is the weighting of components. Assuming that composites are a linear function of their components, composites formed by using standard linear regression are compared to those formed by simple unit weighting schemes, i.e., where predictor variables are weighted by 1.0. The degree of similarity between the two composites, expressed as the minimum possible correlation between them, is derived. This (...) minimum correlation is found to be an increasing function of the intercorrelation of the components and a decreasing function of the number of predictors. Moreover, the minimum is fairly high for most applied situations. The predictive ability of the two methods is compared. For predictive purposes, unit weighting is a viable alternative to standard regression methods because unit weights: are not estimated from the data and therefore do not “consume” degrees of freedom; are “estimated” without error ; cannot reverse the “true” relative weights of the variables. Predictive ability of the two methods is examined as a function of sample size and number of predictors. It is shown that unit weighting will be superior to regression in certain situations and not greatly inferior in others. Various implications for using unit weighting are discussed and applications to several decision making situations are illustrated. (shrink)

A review of the literature indicates that linear models are frequently used in situations in which decisions are made on the basis of multiple codable inputs. These models are sometimes used normatively to aid the decision maker, as a contrast with the decision maker in the clinical vs statistical controversy, to represent the decision maker "paramorphically" and to "bootstrap" the decision maker by replacing him with his representation. Examination of the contexts in which linear models have been successfully employed indicates (...) that the contexts have the following structural characteristics in common: each input variable has a conditionally monotone relationship with the output; there is error of measurement; and deviations from optimal weighting do not make much practical difference. These characteristics ensure the success of linear models, which are so appropriate in such contexts that random linear models may perform quite well. 4 examples involving the prediction of such codable output variables as GPA and psychiatric diagnosis are analyzed in detail. In all 4 examples, random linear models yield predictions that are superior to those of human judges. (shrink)